A shipping box for a refrigerator is shaped like a rectangular prism. The box has a depth of 34,25 Inches (in.), a height of 69,37 in., and a width of 32.62 in. To the nearest hundredth cubic inch, what is the volume of the shipping box?
- A. 2,262.85
- B. 77,502.59
- C. 136.24
- D. 25,834.20
Correct Answer & Rationale
Correct Answer: B
To find the volume of a rectangular prism, multiply its depth, height, and width. In this case, the volume calculation is 34.25 in. (depth) × 69.37 in. (height) × 32.62 in. (width), which equals approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, likely resulting from an incorrect calculation or misunderstanding of the dimensions. Option C (136.24) represents an even smaller volume, which does not align with the dimensions given. Option D (25,834.20) is also incorrect, as it underestimates the overall volume significantly. Thus, only option B accurately reflects the computed volume of the shipping box.
To find the volume of a rectangular prism, multiply its depth, height, and width. In this case, the volume calculation is 34.25 in. (depth) × 69.37 in. (height) × 32.62 in. (width), which equals approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, likely resulting from an incorrect calculation or misunderstanding of the dimensions. Option C (136.24) represents an even smaller volume, which does not align with the dimensions given. Option D (25,834.20) is also incorrect, as it underestimates the overall volume significantly. Thus, only option B accurately reflects the computed volume of the shipping box.
Other Related Questions
The width of a painting is 24 centimeters shorter than its length, x. The area of the painting is 4,081 square centimeters. Which equation could be used to find the dimensions of the painting?
- A. x^2 - 24x - 4,081 = 0
- B. x^2 + 24x - 4,081 = 0
- C. x^2 + 24x + 4,081 = 0
- D. x^2 - 24x + 4,081 = 0
Correct Answer & Rationale
Correct Answer: A
To find the dimensions of the painting, we start with the relationship between length and width. The width is 24 cm shorter than the length \(x\), so it can be expressed as \(x - 24\). The area of a rectangle is given by the product of its length and width, resulting in the equation \(x(x - 24) = 4,081\). Expanding this leads to \(x^2 - 24x - 4,081 = 0\), which matches option A. Option B incorrectly adds 24x, leading to an incorrect area calculation. Option C incorrectly adds 24 and includes a positive constant, which does not represent the area. Option D incorrectly adds 4,081 and has a positive term that does not reflect the relationship between length and width.
To find the dimensions of the painting, we start with the relationship between length and width. The width is 24 cm shorter than the length \(x\), so it can be expressed as \(x - 24\). The area of a rectangle is given by the product of its length and width, resulting in the equation \(x(x - 24) = 4,081\). Expanding this leads to \(x^2 - 24x - 4,081 = 0\), which matches option A. Option B incorrectly adds 24x, leading to an incorrect area calculation. Option C incorrectly adds 24 and includes a positive constant, which does not represent the area. Option D incorrectly adds 4,081 and has a positive term that does not reflect the relationship between length and width.
Solve the inequality for x: -4/3 x + 4 ? 16
- A. x??9
- B. x??9
- C. x??9
- D. x?9
Correct Answer & Rationale
Correct Answer: A
To solve the inequality \(-\frac{4}{3}x + 4 < 16\), first isolate \(x\) by subtracting 4 from both sides, resulting in \(-\frac{4}{3}x < 12\). Next, multiply both sides by \(-\frac{3}{4}\), remembering to reverse the inequality sign, yielding \(x > 9\). Options B and C incorrectly suggest \(x < 9\), which contradicts our solution. Option D, stating \(x \leq 9\), also misrepresents the inequality since it does not include values greater than 9. Thus, only option A accurately reflects the solution \(x > 9\).
To solve the inequality \(-\frac{4}{3}x + 4 < 16\), first isolate \(x\) by subtracting 4 from both sides, resulting in \(-\frac{4}{3}x < 12\). Next, multiply both sides by \(-\frac{3}{4}\), remembering to reverse the inequality sign, yielding \(x > 9\). Options B and C incorrectly suggest \(x < 9\), which contradicts our solution. Option D, stating \(x \leq 9\), also misrepresents the inequality since it does not include values greater than 9. Thus, only option A accurately reflects the solution \(x > 9\).
What is the slope of a line perpendicular to the line given by the equation 5x - 2y = -10?
- A. -0.4
- B. 2\5
- C. 5\2
- D. -2.5
Correct Answer & Rationale
Correct Answer: B
To find the slope of a line perpendicular to the given equation \(5x - 2y = -10\), we first convert it to slope-intercept form (y = mx + b). Rearranging gives \(y = \frac{5}{2}x + 5\), revealing a slope (m) of \(\frac{5}{2}\). The slope of a line perpendicular to another is the negative reciprocal, which is \(-\frac{2}{5}\). Option A (-0.4) is equivalent to \(-\frac{2}{5}\), which is incorrect as it represents a decimal form. Option C (\(\frac{5}{2}\)) is the slope of the original line, not its perpendicular. Option D (-2.5) does not represent the correct negative reciprocal either.
To find the slope of a line perpendicular to the given equation \(5x - 2y = -10\), we first convert it to slope-intercept form (y = mx + b). Rearranging gives \(y = \frac{5}{2}x + 5\), revealing a slope (m) of \(\frac{5}{2}\). The slope of a line perpendicular to another is the negative reciprocal, which is \(-\frac{2}{5}\). Option A (-0.4) is equivalent to \(-\frac{2}{5}\), which is incorrect as it represents a decimal form. Option C (\(\frac{5}{2}\)) is the slope of the original line, not its perpendicular. Option D (-2.5) does not represent the correct negative reciprocal either.
Compare the zeros of function P and function Q. Which statement about the zeros of the functions is true?
- A. Function P has the greater zero, which is 9.
- B. Function P has the greater zero, which is 1.
- C. Function Q has the greater zero, which is 5.
- D. Function Q has the greater zero, which is 4.
Correct Answer & Rationale
Correct Answer: C
To determine which statement is true regarding the zeros of functions P and Q, it's essential to analyze the values given. Option A claims that function P's greater zero is 9; however, this contradicts the provided information, as 9 is not a zero for P. Option B asserts that function P's greater zero is 1, which is also incorrect if 1 is not the highest zero of P. Option D states that function Q's greater zero is 4, but if Q's zeros are higher, this option cannot be true. In contrast, option C correctly identifies that function Q has a greater zero, specifically 5, which aligns with the provided data about the functions' zeros.
To determine which statement is true regarding the zeros of functions P and Q, it's essential to analyze the values given. Option A claims that function P's greater zero is 9; however, this contradicts the provided information, as 9 is not a zero for P. Option B asserts that function P's greater zero is 1, which is also incorrect if 1 is not the highest zero of P. Option D states that function Q's greater zero is 4, but if Q's zeros are higher, this option cannot be true. In contrast, option C correctly identifies that function Q has a greater zero, specifically 5, which aligns with the provided data about the functions' zeros.